Thesis Defense: Strata of residueless meromorphic differentials

This document is a thesis defense announcement for Myeongjae Lee at Stony Brook University. The thesis is titled 'Strata of residueless meromorphic differentials' and focuses on the enumeration and classification of generalized strata of meromorphic differentials. These generalized strata are specific loci within the usual strata of differentials where the sum of certain residues equals zero. They play a role in the boundary of multi-scale compactifications of standard strata. The research presented investigates strata of residueless meromorphic differentials, which represent the most constrained cases regarding residue conditions. The thesis demonstrates that the connected components of these strata can be categorized by established topological invariants: hyperellipticity, spin parity, and rotation number. Furthermore, for one-dimensional projectivized strata, the research provides formulas to calculate the genus of these strata and the degree of their mapping to the moduli of elliptic curves, utilizing the cellular decomposition derived from the period coordinate.